Solution to a differential equation, Mathematics

Assignment Help:

A solution to a differential equation at an interval α < t < b is any function y (t) that satisfies the differential equation in question on the interval α < t < b.  It is significant to note that solutions are frequently accompanied through intervals and these intervals can impart several of significant information regarding the solution.  Consider the subsequent illustration.

Illustration 1:  Show that y(x) = x-3/2 is a solution to 4x2 y′′ + 12xy′ + 3 y = 0 for x > 0.

Solution: We'll require the first and second derivative to do this.

y'(x) = (-3/2) x-5/2                     y''(x) = (15/4) x-7/2

Plug these in addition to the function in the differential equation.

4x2 ((15/4) x-7/2) + 12x((-3/2) x-5/2) + 3(x-3/2) = 0


Related Discussions:- Solution to a differential equation

Curve tracing, how to curve trace? and how to know whether the equation is ...

how to curve trace? and how to know whether the equation is a circle or parabola, hyperbola ellipse?

Find ways in which prizes are distributed between student, Find out the num...

Find out the number of ways in which 5 prizes can be distributed among 5 students such that  (a)   Each student may get a prize. (b)  There is no restriction to the number o

Greatest common factors, Lindy has 48 chocolate chip cookies and 64 vanilla...

Lindy has 48 chocolate chip cookies and 64 vanilla wafers. How many bags can lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bags? She plans

Objectives of why learn mathematics, Objectives After studying this uni...

Objectives After studying this unit, you should be able to explain how mathematics is useful in our daily lives; explain the way mathematical concepts grow; iden

Payoff Matrix, A farmer grows apples on her 400-acre farm and must cope wit...

A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"

Surface area, Find the amount of sheet metal need to form a conical funnel ...

Find the amount of sheet metal need to form a conical funnel of base radius 30cm with a vertical height of 50cm, allowing for 0.5cm overlap. Find the total surface area?

Indeterminate form, Indeterminate form : The 0/0 we initially got is calle...

Indeterminate form : The 0/0 we initially got is called an indeterminate form. It means that we don't actually know what it will be till we do some more work.  In the denominator

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Explain equivalent fractions, Explain Equivalent Fractions ? Two fracti...

Explain Equivalent Fractions ? Two fractions can look different and still be equal. Different fractions that represent the same amount are called equivalent fractions. Ar

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd